Central defender Vitorino Hilton has signed a one-year contract extension with Montpellier.
AC Milan have completed the permanent signing of defender Cristian Zapata from Villarreal for an undisclosed fee.
The England Under-21 international went straight into the North End squad for their League One trip to Crawley on Tuesday night, but the game was later postponed due to a waterlogged pitch.
Rudd has played three cup games for the Canaries this season, including the shock weekend FA Cup defeat to non-league Luton.
Earlier this month, North End cancelled the contract of goalkeeper Steve Simonsen by mutual consent.